An 81-year-old woman died after an ambulance took nearly four hours to reach her home.
She called for an ambulance on Tuesday, saying she had chest pain, but it did not reach her home in Clacton, Essex until three hours, 45 minutes later.
The crew forced entry to home as the control room could not contact the patient and found her dead, the GMB union said.
GMB regional officer Dave Powell said: “There was nothing the crew could do for her.
“The matter has been raised internally as a serious incident and is another example of how we are not coping.
“I’m sure this case is much more widespread than the public is aware of.”
The woman made the emergency call at around 8pm. East England Ambulance Service Trust said “extremely high demand” and delays at A&E prevented them immediately sending an ambulance.
The Trust said there were were 4,200 calls that day, more than 1,300 of which were in Essex and more than 250 were in north east Essex.
A clinician in a control room rang the woman at 9.47pm to check on her. The ambulance crew arrived at 11.46pm.
The Trust said they found the woman unconscious and not breathing.
Sandy Brown, deputy chief executive at East England Ambulance Service Trust said the incident was being investigated and they were “truly sorry” for what happened.
“Our sincere condolences and apologies go out to the patient’s family and friends,” he said.
“We have very publicly expressed how stretched the ambulance service is and the pressures our staff and the NHS as a whole have been under the past few days.
“As a Trust, we have experienced our busiest days ever and we know our partners in the hospitals are in the same situation.
“We are working in partnership but we are facing hospital handover delays, which can prevent us from responding as quickly as we need to.”
It comes after Theresa May apologised for delays to thousands of NHS operations as a result of winter pressures.
Hospitals in England have been told to delay pre-planned operations and routine outpatient appointments until the end of the month due to severe winter pressures.
Officials have estimated that this could lead to up to 55,000 deferred operations.
The prime minister said that while this winter had been “better planned” for than previous years, the delays were “disappointing” and “frustrating”.
Jeremy Hunt acknowledged the health service needed “substantially more resources” in the future.
The health secretary has also been blasted by doctors after he inadvertently admitted this morning that there was a “winter crisis” in the NHS - something he previously had refused to admit was happening.
The cold snap forecast this weekend is likely to mean more strain.
The Met Office has issued a yellow warning for icy conditions on Friday night and into Saturday morning for parts of the north-east of England and Scotland, and in Cornwall, Devon and Somerset, The Press Association reports.
Temperatures are then set to fall on Saturday night due to “cold air and clear skies”, a Met Office spokesman said.
NHS England urged people to stock up on medicines, check on vulnerable or elderly neighbours and get the flu jab, after winter pressures put strain on the health service.
The comments came after it emerged that tens of thousands of planned operations could be delayed for at least a month, as the norovirus and rise in flu levels put pressure on hospitals.
A spokesman said: “Freezing conditions are forecast in some areas and evidence shows that the risk of heart attacks, strokes and other serious breathing problems increases as temperatures plummet.”